Exercises習作簿

古典曲率   (1)Curvature of a cardioid

Differential forms

  1. an action of a  2-form to vectors X and Y

黎曼流形

  1. manifolds   (1)Is SL(2,R) is compact ?  (2)Is the circle simply conneted ?
  2. 向量場
  3. 平行移動
  4. Killing vector field   Jacobi field   (1)A Killing field along a geodesic is a Jacobi field

曲率

  1. Gaussian curvature  (1) Gaussian curvature of a hyperbolic plane (but something wrong)
  2. mean curvature        (2)Willmore inequality for the mean curvature H
  3. Ricci curvature        (1)if Ric(X,Y)=fg then f is constant Here is an exercise of Bianchi identity

測地線

李群